4

Part of 1991 Swedish Mathematical Competition

Problems(1)

moves on a permutation of 1, 2, ..., 8

Source: 1991 Swedish Mathematical Competition p4

x_1, x_2, ... , x_8

is a permutation of

1, 2, ..., 8

. A move is to take

x_3

x_8

and place it at the start to from a new sequence. Show that by a sequence of moves we can always arrive at

1, 2, ..., 8

combinatoricspermutation